With iOS 8, you don't need to install any apps to upload a photo to Facebook -- the system has Facebook sharing built in. If you do have the Facebook app, upload your picture from within the app for a few additional features, such as adding stickers to the image.
Upload Without Facebook App
If you haven't used Facebook on your phone yet, you need to sign in first. Open the Settings app to the Facebook tab and log in.
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Run the Photos app and open the image you want to upload. Tap the Share icon in the lower left corner and select Facebook.
Upload With Facebook App
Press Photo at the top of your News Feed in the Facebook app. Select one or more pictures and press Done, or, to take a new picture, tap the camera icon.
At the bottom of your photo, tap the smiley face to add stickers or the Aa icons to add text atop the image. Below the image, there's a row of icons for additional optional features.
In order, these icons are:
After you're all set, scroll to the top of the page.
Add status text in the Say Something... field above the image. Tap To if you want to select a different audience. When you're finished, tap Post to upload the image.